Electrostatic support

ABSTRACT

1. AN ELECTROSTATIC SUPPORT SYSTEM FOR SUPPORTING A MEMBER BETWEEN A PAIR OF ELECTRODES COMPRISING IN COMBINATION: ELECTROSTATIC SUPPORT CIRCUIT ESTABLISHING AN ALTERNATING POTENTIAL BETWEEN SAID MEMBER AND SAID ELECTRODES FOR ELECTROSTATICALLY SUPPORTING SAID MEMBER, SENSING MEANS PROVIDING AN ALTERNATING SIGNAL INDICATIVE OF THE DISPLACEMENT OF SAID MEMBER FROM A CENTERED POSITION BETWEEN SAID PAIR OF ELECTRODES, AND NEGATIVE IMPEDANCE MEANS RESPONSIVE TO SAID ALTERNATING SIGNAL AND PROVIDING A SIGNAL TO SAID ELECTROSTATIC SUPPORT CIRCUIT VARYING SAID ALTERNATING POTENTIAL BETWEEN SAID MEMBER AND SAID ELECTRODES SO AS TO EFFECT SUBSTANTIAL CENTERING OF SAID MEMBER BETWEEN SAID PAIR OF ELECTRODES.

Jun. 5, 1'73 ATKINSON RC. 27,560

ELECTROSTATIC SUPPORT Original Filod llarch 7, 1966 2 Sheets-Sheet 1FIG. I

INVENTOR.

JAMES L ATKINSON Jill" 1 73 J. L. ATKINSON Rt 27,560

ELECTROSTATIC SUPPORT Original Filed larch '7, 1966 2 Sheets-Sheet 3 (kv 0 FIG. 2

FIG. 3

I c T J 2T FIG.4

b g 4,. if I FIG. 5

INVENTOR.

JAMES L. ATKINSON ma/W United States Patent Office Reissued June 5, 197327,660 ELECTROSTATIC SUPPORT James L. Atkinson, La Mirada, Califl,assignor to North American Rockwell Corporation Original No. 3,411,838,dated Nov. 19, 1968, Ser. No. 532,371, Mar. 7, 1966. Application forreissue Apr. 8, 1970, Ser. No. 26,548

Int. Cl. F16c 39/06 U.S. Cl. 308- 7 Claims Matter enclosed in heavybrackets appears in the original patent but forms no part of thisreissue specification; matter printed in italics indicates the additionsmade by reissue.

This invention relates to an electrostatic support and more particularlyto a semi-passive electrostatic support for supporting the rotor of agyroscope.

In the prior art of electrostatic supports there presently exists twomajor categories for maintaining the rotor or supported member, in thepresence of disturbing forces, centered or servoed between thesupporting electrodes. These categories are active compensation andpassive compensation. One technique used under the active compensationcategory is the two-frequency scheme in which one frequency is used tosense position and the other to control position. A two-frequency schemeis disclosed in us. Patent No. 3,003,356, entitled, Free-Gyro Systemsfor Navigation or the Like, by A. T. Nordsieck. The other technique usedin active compensation is the cancellation or undirectional scheme inwhich position information is separated from control information. Acancellation scheme is disclosed in US patent application Ser. No.443,539, entitled Electrostatic Bearing," filed Mar. 29, 1965, by JamesL. Atkinson, the inventor of the present device.

The active compensation support systems require complex electronicswhich create packaging, reliability, power and adjustment problems.

In passive compensating supports no attempt is made to determineposition information. One such system is disclosed in US. Patent No.3,098,679, entitled Passive Control Circuit for Electrostatic Bearing"by William F. De Boice. The disadvantage of this type of support is thatit works only in a fractional g environment, that is, it cannot functionunder heavy g environments such as in experienced in missiles and otheraircraft.

The semi-passive support of the present invention blends together theadvantages of both the active and passive categories wherein no attemptis made to sense position explicitly. Amplifiers, such as may be foundin an active system are used to decouple stiffness and damping which areclosely interdependent in the strictly passive system. This results in aset of electronics which uses a minimum of electrical components.

It is therefore an object of this invention to provide an improvedelectrostatic support system.

Another object of this invention is to provide a semipassiveelectrostatic support system which combines the advantages of passiveand active support systems.

Still another object of the present invention is to provide anelectrostatic support system which utilizes negative impedanceconverters.

These and other objects of the invention will become more apparent fromthe following description when taken in conjunction with the drawings inwhich:

FIG. 1 illustrates an electrostatic support system embodying theinvention;

FIG. 2 is a passive circuit which may he used with the presentinvention;

FIG. 3 is a schematic presentation of an equivalent circuit which may beused with the invention;

FIG. 4 is a schematic presentation of an equivalent circuit which may beused as part of the circuit of FIG. 3; and

FIG. 5 is a combined passive and active circuit which may be used withthe present invention.

In FIG. 1 a three-axis support for an electrostatic gyroscope having aconductive spherical rotor 10 is shown. The sphere 10 iselectrostatically supported by electrode plates 15 and 16 in onedirection, electrode plates 13 and 14 in another direction, andelectrode plates 11 and 12 (not shown) in still another direction so asto provide a three-dimensional support. In the specific embodimentillustrated the above respective pairs of plates are shown symbolicallyas being circular and equally spaced around the periphery of the sphere10. It will be understood that the plates may take various shapes andthat such would be only a function of design. In addition, the innersurfaces of the plates will preferably be concave and concentric withthe center of the sphere 10. Plates 11 through 16 have inner surfaceswhich define a sphere which is slightly larger and concentric withsphere 10.

The power supporting circuit 20 is connected to plates 11 and 12 forelectrostatically supporting the sphere 10 between plates 11 and 12. Asensing and servo circuit 30 is coupled by the transformer T to thepower supporting circuit 20 so as to effect centering of the sphere 10between the plates 11 and 12. That is, if the sphere 10 tends to not becentered between plates 11 and 12, the sensing and centering circuit 30will effect application of a signal through the power circuit 20 to theplates 11 and 12 so as to center the sphere therebetween. The electrodes13 and 14 are connected to the power supporting circuit 40 forsupporting the sphere 10 between the electrodes 13 and 14. The sensingand servo circuit 50 is coupled by the transformer T to the powersupporting circuit 40 so as to sense when the sphere 10 is not centeredbetween the electrodes 13 and 14 and in response thereto to apply asignal to the power circuit 40 to effect the centering of the sphere 10between the electrodes 13 and 14.

The electrodes 15 and 16 are connected to the power supporting circuit60 for supporting the sphere 10 between electrodes 15 and 16. Thesensing and servo circuit 70 is coupled through the transformer T to thepower circuit 60 so as to effect centering of the sphere 10 betweenelectrodes 15 and 16.

The sphere 10 is an electroconductive sphere made of some material suchas aluminum. In the preferred form shown in the drawing, a three-phaseconstant current power current supply through conductors 81, 82 and 83provides power in three phases through the power circuits 20, 40 and 60to electrostatically suspend the sphere 10. More specifically, conductor81 is connected to provide a current to the center tap of the secondarywinding of transformer T of circuit 20. Conductor 82 provides a currentdegrees out of phase with conductor 81 and conductor 83 and is connectedto the center tap of the secondary winding of transformer T of circuit40. Conductor 83 provides a current which is 120 degrees out of phasewith the current in conductors 81 and 82, and is connected to the centertap of the secondary winding of transformer T of circuit 60.

Thus, by the connections between the three-phase power supply 80 and thepower circuits 20, 40 and 60, sufliclent voltage appears between theelectrode plates and the sphere so as to normally, with the aid ofsensing and servo circuits 30, 50 and 70, to electrostatically supportthe sphere in three dimensions.

Means well known to those skilled in the art may be used to rotate thesphere 10 at a high rate of speed such that it displays thecharacteristics of a gyroscope.

Such means for rotation form no part of the present invention.

The power circuit 40 and the sensing and servo circuit 50 which areutilized to electrostatically support and center the sphere betweenplates 13 and 14 are numbered in detail in the drawing.

Since the power circuits and 60 along with sensing and servo circuits 30and 70, respectively, are identical to the power supporting circuit 40and the sensing circuit 50, respectively, only the latter will bedescribed in detail.

As shown in FIG. 1, the secondary of transformer T is center tapped at43 so as to divide this winding into two equal windings 41 and 42. Thesewindings are poled as shown by the dots and have their outer endselectrically connected to the plates 13 and 14.

Due to the AC. currents applied through conductors 81, 82 and 83 totheir respective plates, the conductive sphere 10 will be maintained atA.C. ground. Thus, a current from conductor 82 will flow throughwindings 41 and 42, plates 13 and 14, respectively, and thence throughthe conductive sphere 10 back to ground. When the sphere 10 is centeredor equidistant from plates 13 and 14, the two branch currents i and ipassing through windings 41 and 42, respectively, will be equal. Whenthese currents are equal and the sphere 10 is centered between theplates there will be no current induced back into the primary winding 44of transformer T The sensing and servo circuit 50 includes the primarywinding 44 which has one end grounded and the other end connected to thepoint A. A non-inverting amplifier 53 has its input connected to point Aand is electrically referenced to ground. A feedback capacitor 54 isconnected from the output of amplifier 53 to the point A. The input ofthe non-inverting amplifier 57 is connected to point A by resistor 55.Amplifier 57 is electrically referenced to ground. Capacitor 56 isconnected from the input of amplifier 57 to ground. Capacitor 59 andresistor 58 are serially connected from the output of amplifier 57 tothe input of amplifier 57. The impedance from point A to ground lookingtowards the amplifiers 53 and 57 is designated Z. The amplifiers 53 and57 in combination with their associated passive capacitors and resistorsform two negative impedance converters, the function of which will behereinafter described.

The electrostatic support system is inherently unstable and will notsupport the sphere 10 unless a proper stabilization device or circuit isconnected to point A.

When the sphere 10 is disturbed by some external force it will operateas a balanced modulator providing a double size band suppressed carrieroutput signal at point A.

In the present invention it may be shown that by providing the correctvalue of Z from the point A to ground, the system will be stable andprovide for the centering of the sphere between the plates for a widerange of applied force. It has also been found that utilization of thepresent invention provides a capability of independent adjustment ofstiffness and damping. As will be shown, Z is not positive real; thiscondition requires that negative impedance converters be used tosynthesize the driving point impedance Z.

Definition of terms The following terms are now defined and will be usedthroughout the remaining description of the invention.

V =the voltage across winding 41,

V =the voltage across winding 42,

V =the voltage between the center tap 43 and ground,

V =the voltage across winding 44,

N /N =the turns ratio between windings 41 and 42; it

equals 1 for the specific embodiment shown,

N /N =the turns ratio between winding 44 and winding 41,

C =the capacitance between electrode 13 and sphere 10, which is equal tothe capacitance between electrode 14 and sphere 10, when the sphere iscentered between the electrodes,

C =the capacitance between electrode 13 and sphere 10, when the sphereis not centered between electrodes 13 and 14,

i =i +i where i is the current through winding 41 and i is the currentthrough winding 42,

i =the current through winding 44,

e :relative displacement of the sphere from its central position,

K=damping factor,

K stiffness factor,

s Laplace operator,

w :radian frequency of supply 80.

Analysis For simplicity of analysis, it is assumed that transformer T isideal, that is, that N =N magnetizing inductance is infinite and leakageinductance and losses are zero. For this transformer Taking theKirchholfs equation around the loop defined by i we obtain:

1 ca e;

(1.4) Substituting Equation 1.4 into Equation 1.3, we obtain:

The equation for the loop defined by i is similar to Equation 1.5.

T 5 (1.6) Solving Equation 1.5 and Equation 1.6 for V 2 l z-lr 200s 200s(1.7

Substituting the value of V in Equation 1.2 we obtain:

and substituting Equation 1.9 into Equation 1.10 and rearrangingNormalized force equation and dummy transfer function It is nownecessary to obtain the net normalized force F acting on the sphere fromplates 13 and 14.

5 Substituting Equation 1.11 into Equation 2.2

1 'zcs 1" 2.3

From Equation 2.3 a dummy transfer function N(s) may be obtained:

1 zc.s+1 2.4) In the servo art stability or damping can be achieved by asimple lead compensation, therefore, N(s) will take the form of an A.C."notch network as illustrated in FIG. 2.

The transfer function of the network of FIG. 2 is Los=+ 5+1 e R LCs+(-8+]. (2.5) Let P 1 R w.,Q (2.6) and n 3 R1 R mQ (2.7)

and

l FJ (2.8) To increase the stiffness of the circuit and additional gainfactor K, is added such that Q (2.9) Solving Equations 2.4 and 2.9 for Zwe obtain:

23 K5 .l. l-l-K w," l-l-K Q 1, K (Ls s 1 s d gg 3+ (2.10)

Thus Z is not positive real and must be synthesized with negativeimpedance converters.

Synthesis of Z FIG. 3 is the schematic equivalent of Equation 3.2. Fromthis equivalent circuit 6 Let as-i-b Z,-,1- 1+Z4 (3.9)

where as+b Rearranging Z in product form 1 as+b)( l b s s 3.11

Let

as-i-b 8 (3.12)

and

Z and Z are selected such that their equivalent parallel impedance isproportional to the product of their impedances, that is,

From Equations 3.4 and 3.9 we obtain:

The equivalent circuit for Equation 3.16 is shown in FIG. 4.

The completed equivalent circuit for Z is shown in FIG. 5 and again inFIG. 1, where and the negative impedance converters 53 and 57 providefor the negative signs in Equations 3.16 and 2.10.

In practice, the following real values were used:

Resistor 55:6.05 K ohm-s, Resistor 58:18.3 ohms, Capacitor 54=.l8;tfd.Capacitor 56:.0074 ,ufd. Capacitor 59:.0074 fd.

The gain of amplifiers 53 and 57=+2; w =Z0 kc.

Independent adjustment of stiffness and damping is achieved by varyingthe values of K for stiffness and K for damping.

Although the invention has been described and illustrated in detail itis to be understood that the same is by Way of illustration and exampleonly and is not to be taken by way of limitation, the spirit and scopeof this invention being limited only by the terms of the appendedclaims.

I claim:

1. An electrostatic support system for supporting a member between apair of electrodes comprising in combination:

electrostatic support circuit establishing an alternating potentialbetween said member and said electrodes for electrostatically supportingsaid member; sensing means providing an alternating signal indicative ofthe displacement of said member from a centered position between saidpair of electrodes; and

negative impedance means responsive to said. alternating signal andproviding a signal to said electrostatic support circuit varying saidalternating potential between said member and said electrodes so as toeffect substantial centering of said member between said pair ofelectrodes.

2. The electrostatic support system of claim 1 wherein said providedsignal of said impedance means is reflected through said sensing meansto said electrostatic support circuit.

3. The electrostatic support system of claim 2 wherein said sensingmeans is a transformer having a primary and a secondary winding, theprimary winding of said transformer connected to said electrodes so asto sense the current flow between said electrodes and said supportedmember, the secondary of said transformer connected to said impedancemeans.

4. The electrostatic support system of claim 1 wherein said impedancemeans is a negative impedance.

5. The electrostatic support system of claim 4 wherein said negativeimpedance is generated by negative impedance converters. 1

6. The electrostatic support system of claim 3 wherein said impedancemeans comprises a first amplifying means connected across saidtransformer secondary winding, a first capacitor connected from theoutput to the input of said amplifying means, a second amplifying meansconnected across said transformer secondary winding, a second capacitorconnected in series with a resistor from the output to the input of saidsecond amplifier means, said amplifying means converting the values ofsaid resistors and capacitors to negative values.

7. The support system of claim 1 wherein said impedance means is a leadcompensation network having a nega tive transfer impedance.

References Cited The following references, cited by the Examiner, are ofrecord in the patented file of this patent or the original patent.

UNITED STATES PATENTS 3,262,325 7/1966 Senstad 308-10 3,262,326 7/1966Schott 308- ROBERT SKUDY, Primary Examiner

